Tim Lee was a senior in college five years ago when he registered the domain name Cool.com, almost on a lark. Friends scoffed, but Lee may be getting the last laugh: He says he recently got an offer for the name worth up to $38 million.

Lee turned down what would have been a record price for a domain name, although he and his partner say they are still considering some kind of partnership with the investor, whom they would not identify. Lee says they were unable to accept the offer because by then they already had agreed to take $1 million from a venture capital firm in exchange for an undisclosed stake in their company.

In any case, after five years of rebuffing steadily rising offers for an asset that cost him nothing to acquire, Lee, 28, finally quit his day job this month to devote himself full-time to building the URL into a business he hopes one day will be worth far more.

"The timing is right," Lee said.

When Lee first registered the Cool.com name, the Web was in its infancy and friends at the University of Washington wondered why he would bother, even though domain names cost nothing to register at the time.

"I was bragging that I got this cool domain, and people asked me, 'Why would you want a domain? What are you going to do with it?' " Lee said.

At the time, Lee had no real idea, and it would not have taken much to get him to give up his rights and forget all about it.

"All I wanted was enough money to pay off my school loans and make a nice down payment on my house," Lee said. "I would have sold it for less than $100,000."

Instead he got offers of a few hundred to a few thousand dollars, nothing he considered serious.

So he bided his time, managing a data center for an Internet service provider and occasionally leasing the domain name to companies for special events, never getting more than $1,000 for a one-month run.

Lee said he got his first offer in 1996 and typically fielded about two cold calls a month, including one from Adam Curry, a broadcast personality who reportedly got $1 million for rights to the MTV.com domain name in a celebrated mid-1990s court case.

For a while, Lee loaned out the name to other entrepreneurs for six months at a time, hoping they would be able to develop a business plan compelling enough to persuade him to invest his increasingly valuable asset. Nothing came of those efforts, and in July 1999 he incorporated the business and began developing a business plan with Greg Olsby, a colleague from his years working at the ISP, now known as Winstar.

The pair put up a simple "splash screen" with the Cool.com name, and people began flocking to it by the thousands, although there had been no publicity and the site had no content -- meaning visitors were simply typing the world "cool" into their browser or search engine. A survey form asked users to describe themselves, and 75 percent of the respondents said they were teenagers, said Olsby.

So the decision was made to focus on "Generation Y," the highly desirable 12-to-22-year-olds who are the fastest-growing and most Web-savvy segment of the U.S. population.

"This group has been underserved to begin with," said Olsby, a 43-year-old father of three who admits to being well outside the "cool" demographic. "Most of the Internet focus has been on the baby boomers and Generation X, and this population is twice as big as the baby boom generation."

Lee and Olsby plan to turn Cool.com into an "infomediary," providing valuable market research to partner companies on the attitudes of its target audience. Revenues also could come from advertising, sales of products such as music and apparel, and ultimately by offering to establish turnkey stores under the Cool.com umbrella.

So far the site is offering free e-mail, chat and and a few lightly trafficked bulletin boards. The company has only three employees, although Lee and Olsby hope to ramp up quickly now that they have raised an initial $1.3 million.

It's not exactly uncharted territory. Just last week Snowball.com, which operates Web sites targeted at the same demographic group, went public and was greeted with little enthusiasm by investors. Rival Bolt.com and MTV's Internet unit also are expected to go public with similar business plans.

Nevertheless, Olsby and Lee have been getting impressive offers for their company, including one for $1 million that was rejected flat out several weeks ago.

"It was not something I was interested in," Lee said matter-of-factly. "A million dollars is not a whole lot lot these days."

Among the potential buyers have been Continental Airlines, for its Continental On Line operation; Cyberian Outpost, which uses COOL as a ticker symbol; and an executive for a major search engine company, Lee said.

Then came an offer from a New York lawyer, representing a consumer products marketing company, who offered $3 million cash. Last week, he upped the ante to $8 million plus a potential $30 million worth of stock.

"It's tempting," Lee admitted. "But the opportunities for using such a brand for marketing and a long-term business strategy are a lot more compelling. Long term, we have an opportunity to really develop a global brand that is a force to be reckoned with."

It is not inconceivable that a savvy marketer would pay upward of $10 million for a site with such built-in name recognition, said Jeffrey Tinsley, chief executive officer of GreatDomains.com, a domain name broker.

"This is happening more and more frequently, as companies are realizing how important it is to start out with a good name," he said. "Sites like Cool.com already have built-in traffic. It’s a great name -- it's a common term, and it's short."

Last year, eCompanies in Santa Monica, Calif., paid $7.5 million for the rights to the Business.com domain name, which remains the highest price on record, although there have been several verified sales of $2 million or more.

Currently GreatDomains.com lists at least two sites for sale in the $10 million range. He said the owner of America.com has rejected offers "in excess" of $10 million. The current asking price is listed as $30 million.

Also listed for sale on GreatDomains.com is -- you guessed it -- www.cool.com. The price? "Make offer."

Olsby said the company may have asked the broker for an appraisal but never authorized him to list the site for sale.

"You know how it is," said Olsby, a little apologetically. "Sometimes a broker will call you up with an offer to buy your house."